Entanglement Dynamics between Ising Spins and a Central Ancilla

TL;DR

This paper studies the entanglement dynamics in an open Ising-spin chain coupled to a central ancilla, revealing how ancilla entanglement entropy correlates with phase transitions and quantifies entanglement loss.

Contribution

It introduces the multipartite entanglement loss (MEL) as a new measure linking spin-fluctuations, quantum Fisher information, and entanglement entropy in composite quantum systems.

Findings

Ancilla entanglement entropy tracks dynamical phase transitions.

MEL is proportional to the exponential of ancilla entanglement entropy.

Pure spin chain limit corresponds to zero MEL.

Abstract

We investigate competing entanglement dynamics in an open Ising-spin chain coupled to an external central ancilla qudit. In studying the real-time behavior following a quench from an unentangled spin-ancilla state, we find that the ancilla entanglement entropy $S_{vN;\mathcal{A}}$ tracks the dynamical phase transition in the underlying spin system. In this composite setting, purely spin-spin entanglement metrics such as mutual information and quantum Fisher information (QFI) decay as the ancilla entanglement entropy grows. We define multipartite entanglement loss (MEL) as the difference between collective magnetic fluctuations and QFI, which is zero in the pure spin chain limit. MEL directly quantifies the ancilla's effect on the development of spin-spin entanglement. One of our central results is that $MEL(t) \propto e^{S_{vN;\mathcal{A}}(t)}$. Our results provide a platform for exploring composite system entanglement dynamics and suggest that MEL serves as a quantitative estimate of information entropy shared between collective spins and the ancilla qudit. Our results present a new framework that connects physical spin-fluctuations, QFI, and bipartite entanglement entropy between collective quantum systems.